Duke starting quarterback Sean Renfree missed the game with an injured right elbow, and Boone threw for 212 yards without an interception in relief.
The victory gave Duke (5-1, 2-0) its best start to the season since the 1994 team won its first seven games.
The key stretch of the game came early in the third quarter.
The Cavaliers had a 17-14 halftime lead on the strength of a first half where they averaged 7.1 yards per rush and totaled 184 yards on the ground.
After going without any yards on its first drive of the second half, Virginia had to punt from its own 5-yard line. Vernon returned the punt all the way to the Cavaliers' 22, and a holding penalty that was added on to the punt return gave Duke the ball at Virginia's 12.
Boone then lofted a swing pass to a wide-open Juwan Thompson for a touchdown on the Blue Devils' first play of the drive, giving Duke a 21-17 advantage.
The Blue Devils defense then stopped Kevin Parks on a fourth-and-1 from Virginia's 47-yard line on the Cavaliers' ensuing possession.
Duke took advantage of its optimal field position, gaining the 45 yards in four plays. Jela Duncan finished the drive with a powerful 11-yard touchdown run to go up by 11 points.
The only scoring of the fourth quarter came when Vernon caught a 45-yard high-arcing pass from Boone and when Thompson had a 34-yard touchdown rush for the final margin.